Quantitative Finance > Trading and Market Microstructure

Abstract: We consider idealized financial markets in which price paths of the traded
securities are cadlag functions, imposing mild restrictions on the allowed size
of jumps. We prove the existence of quadratic variation for typical price
paths, where the qualification "typical" means that there is a trading strategy
that risks only one monetary unit and brings infinite capital if quadratic
variation does not exist. This result allows one to apply numerous known
results in pathwise Ito calculus to typical price paths; we give a brief
overview of such results.